Print Email Facebook Twitter Single-qubit dynamics Title Single-qubit dynamics: Determining the density matrix of a qubit in closed and open quantum systems when considering free evolution and weak measurements Author Witmer, Brian (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Applied Sciences) Contributor Blanter, Y.M. (mentor) Caspers, M.P.T. (graduation committee) Thijssen, J.M. (graduation committee) de Laat, D. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics | Applied Physics Date 2022-08-11 Abstract Quantum technology is evolving faster than ever. Currently, all eyes are on the quantum computer, the promising computer that can solve problems which are unsolvable for regular computers. In order to understand this new technology, it is necessary to understand the qubit, the basic unit of quantum information. This can be done by means of the density matrix: a mathematical representation of the state of a system. The aim of this thesis is to find the density matrix of a single qubit in closed (isolated) and open quantum systems. In the case of a closed system, an alternating sequence of two processes with different Hamiltonians is considered, which both last a fixed amount of time after one another. These systems have been solved using a direct formula for a 2 × 2 matrix with distinct eigenvalues raised to the power n for any n ∈ N. In the case of an open system, dissipation is taken into account compared to a single process in a closed system. These open systems have been solved numerically using the Lindblad master equation and the spin-boson model to model the environment as a bath of bosons. However, the use of multiple approximations and assumptions questions the validity of the results for ’strong’ interactions. Suggestions for further research include investigating quantitatively when the Lindblad equation is valid to use and solve open quantum systems using different models for the environment. Subject Quantum MechanicsQubitsDensity matrix To reference this document use: http://resolver.tudelft.nl/uuid:645f0f30-25b6-4b81-8b0d-a304b23b38a8 Part of collection Student theses Document type bachelor thesis Rights © 2022 Brian Witmer Files PDF BEP_Brian_Witmer_final.pdf 960.34 KB Close viewer /islandora/object/uuid:645f0f30-25b6-4b81-8b0d-a304b23b38a8/datastream/OBJ/view